In securing victory, Connacht moved above Edinburgh and into ninth place and are now just three points adrift of Treviso in eighth.
And Elwood believes his side can now string a series of results together.
"We've set our own targets and goals and points that we're looking for and this win has gone a long way in putting things right," Elwood told the Irish Examiner.
"We have an opportunity next week in Cardiff and then we come back the following week at home to Zebre.
"So there's still good challenges, good opportunities ahead of us and certainly four points [against Ospreys] will help.
"We were playing against a good team who beat Ulster last week - their first defeat at home - and we out-played them.
"And that was the type of intensity we're trying to train at and play at."
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